Step |
Hyp |
Ref |
Expression |
1 |
|
normcl |
|
2 |
1
|
resqcld |
|
3 |
2
|
recnd |
|
4 |
3
|
addid1d |
|
5 |
4
|
adantr |
|
6 |
|
normcl |
|
7 |
6
|
sqge0d |
|
8 |
7
|
adantl |
|
9 |
6
|
resqcld |
|
10 |
|
0re |
|
11 |
|
leadd2 |
|
12 |
10 11
|
mp3an1 |
|
13 |
9 2 12
|
syl2anr |
|
14 |
8 13
|
mpbid |
|
15 |
5 14
|
eqbrtrrd |
|
16 |
15
|
adantr |
|
17 |
|
normpyth |
|
18 |
17
|
imp |
|
19 |
16 18
|
breqtrrd |
|
20 |
19
|
ex |
|
21 |
1
|
adantr |
|
22 |
|
hvaddcl |
|
23 |
|
normcl |
|
24 |
22 23
|
syl |
|
25 |
|
normge0 |
|
26 |
25
|
adantr |
|
27 |
|
normge0 |
|
28 |
22 27
|
syl |
|
29 |
21 24 26 28
|
le2sqd |
|
30 |
20 29
|
sylibrd |
|